Step-by-step explanation:
Do it please mmm m mm mmm mm
1 answer:
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The functions are:
i)
ii)
.
We note that both Sin and Cos functions cannot produces values smaller than -1, or larger than 1.
In other words, the range of both these functions is [-1, 1].
Whatever expression A is, sin(A) and cos(A) are values in [-1, 1].
Assume
produced its maximal value, 1, then 
makes this value 3.
Thus, the maximum value of g(x) is 3, as can be also seen in the graph.
Similarly, assume cos(x) produced 1, then 2cos(x) makes it 2. Thus, the greatest value of f(x) is 2.
Answer: max{f(x)}=2, max{g(x)}=3, so g has the largest maximal value.
i)
ii)
We note that both Sin and Cos functions cannot produces values smaller than -1, or larger than 1.
In other words, the range of both these functions is [-1, 1].
Whatever expression A is, sin(A) and cos(A) are values in [-1, 1].
Assume
Thus, the maximum value of g(x) is 3, as can be also seen in the graph.
Similarly, assume cos(x) produced 1, then 2cos(x) makes it 2. Thus, the greatest value of f(x) is 2.
Answer: max{f(x)}=2, max{g(x)}=3, so g has the largest maximal value.
Answer:
13.57 kg
Step-by-step explanation:
Let the amount of salt in a tank be =
=
= 0.3 kg/L
The concentration of salt coming into the tank = 0.333kg/L
We know that the concentration of salt leaving the tank should be:
amount of salt in the tank/volume of tank = y(t)/50 L
rate of change of salt = rate in - rate out
= 0.66 -
solving the differential equation gives :
ln y = 0.66/y (t) - 0.02 t + C
Initial conditions, t= 0; y (0) = 15
then ln 15 = C
ln y = t - 0.02t + ln 15
ln = 0.02t
y = 15e( exp -0.02t)
the amount of salt in 5 mins will be:
y (t) = 15e(exp -0.02 (5)
= 13.57 kg